Electromagnetic radiation concentrating apparatus embodying frustoconical mirror elements

ABSTRACT

1,110,821. Aerials. C. JACOBSEN &amp; CIE. 4 May, 1965 [6 May, 1964], No. 18822/65. Heading H4A. [Also in Divisions F4 and G2] An electromagnetic radiation concentrator, particularly for use in the infra-red, comprises a front system 9, Fig. 1, of relative aperture 1 - which forms an image of the source in its N focal plane 10, the maximum inclination # 1  to the axis of the system of rays forming the image 1 being such that sin # 1 #-, and at least one 2N trunco-conical element 11 of internal refractive index n 1  and apex half-angle &amp;gamma; of 0À1 radian or less, which converges the beam by internal reflections on its trunco-conical surface, the entry surface 12 of element 11, having the maximum diameter d 1  being disposed in coincidence with image plane 10 and the minimum diameter d x  being associated with a sensitive element 14 immersed in a medium 15 of refractive index n 2  wherein: p&lt;SP&gt;1&lt;/SP&gt; being the maximum number of internal reflections experienced by a ray forming the maximum angle # 1  with the optical axis before entering the element 11 and given by: # 1  being given by: n 1 , n 2 , sin # 1  and tan &amp;gamma; also being connected by the relationship: wherein # denotes the minimum efficiency required relatively to the maximum possible n&lt;SP&gt;2&lt;/SP&gt; 2  defined by -. The front system 9 may be a sin&lt;SP&gt;2&lt;/SP&gt;# 1  lens, concave mirror (16), Fig. 2 (not shown), or solid trunco-conical member 105, Fig. 10 (not shown), with a convex front surface. In the latter case the optical axis 106 may be deflected through 90 degrees by means of a 45 degrees surface 107. The element 11 may be hollow or solid in which case the reflections on its surface are all total internal reflections and p&lt;SP&gt;1&lt;/SP&gt; must be equal to or less than # wherein: n 1 , sin # 1  and &amp;gamma; also being connected by the relationships: The trunco-conical element 11 may be formed from several materials placed end-to-end, or made from a series (26), Fig. 3 (not shown), of parallel fibres (27). Scanning may be used in association with the device, Fig. 6 (not shown), and an application to centimetre radar, Fig. 5, is described in which the front system is a parabolic mirror 60, the trunco-conical element 61 is of aluminium and the sensitive element 59 is a dipole antenna having an effective diameter of 0À5 cm. Detailed steps are enumerated for designing specific systems.

Oct. 20, 1970 p, MAUFAUD 535,016

ELECTROMAGNETIC RADIATION CONCENTRATING APPARATUS EMBODYING FRUSTOCONICAL MIRROR ELEMENTS Filed April 28, 1965 8 Sheets-Sheet 1 59. 3 INVENTOR.

PIERRE MALIFAUD Oct; 20, 1970 L D 3,535,016

ELECTROMAGNE R ATION CENTRATING APPARATUS EMBODY FRUSTOCONI MIRROR ELEMENTS Filedltpril 28, 1965 8 Sheets-Sheet 2 Hg. 7 fig. 9 I

INVENTOR. PIERRE MALIFAUD Oct. 20, 1970 P. MALIFAUD 3,535,016 ELECTROMAGNETIC RADIATION CONCENTRATING APPARATUS EMBODYING FRUS'IOCONICAL MIRROR ELEMENTS Filed April 28, 1965 8 Sheets-Sheet 5 INVENTOR. PIERRE MALIFAUD Oct. 20, 1970 MAUFAUD 3,565,016

ELECTROMAGNETIC RADIATION CONCENTRATING APPARATUS EMBODYING FRUSTO'CONICAL MIRROR ELEMENTS Filed April 28, 1965 8 Sheets-Sheet L INVENTOR. PIERRE MALIFAUD Oct. 20, 1970 ELECTROMAGNETIC RADIATION CONCENTRATING APPARATUS EMBODYING FRUSTOCONICAL MIRROR ELEMEN Filed April 28, 1965' P. MALIFAUD 3,535,016

8 Sheets-Sheet 5 a o N @E a;

n s 7 3 at & -INVENTOR.

PIERRE MALIFAUD BY A l Oct. 20, 1970 P. MALIF'AUD ELECTROMAGNETIC RADIATION CONCENTRATING APPARATUS Filed April 28. 1.965

8 SheetsSheet 6 42 40 INVENTOR. 44 38 PIERRE MALIFAUD Oct. 20,1970

P. MALIFAUD 3,535,016 ELECTROMAGNETIC RADIATION CONCENTRATING APPARATUS EMBODYING FRUSTOCONICAL MIRROR ELEMENTS Fil9d April 28, 1965 8 Sheets-Sheet 7 INVENTOR. PIERRE MALI FAUD BY j Oct. 20, 19 0 P. MALIF'AUD w 3 3 ELECTROMAGNETIC RADIATION CONCENTRATING APPARATUS EMBODYING FRUSTOCONICAL MIRROR ELEMENTS Filed April 28, 1965 8 Sheets-Sheet 8 I NVEN TOR.

PIERRE MALIFAUD BY .7

United States Patent Int. Cl. (021) /14 US. Cl. 350-96 3 Claims ABSTRACT OF THE DISCLOSURE Apparatus for the concentration of electromagnetic energy of all kinds with maximum efliciency comprises one or more frustoconical internally reflecting elements, arranged serially if there are more than one, associated with a frontal optical concentrating device or system delivering radiation at the maximum cross section of the frustoconical element or elements and with a radiation sensing element positioned at the minimum cross section of the frustoconical element or elements. The optical half-angle of the frustoconical element is of the order of A radian as a maximum. It concentrates radiation entering its larger face from the frontal element by internal reflection to a maximum concentration at its smaller face where the radiation is passed to the sensing element. A preferred form of the frustoconical elements for concentrating light waves are bundles of conical fibers over the range of the spectrum for which material transparent to the wave-lengths concerned and formable into conical fibers is available. The frustoconical element may consist of a plurality of frustoconical members serially arranged with the minimum diameter face of the first coincident with the maximum diameter face of the next in series. The frustoconical members may be cut at suitable angles and sections folded back on each other at the cut faces to conserve space.

The invention comprises apparatus for the maximum concentration of electromagnetic radiation of all kinds in cluding visible, ultraviolet and infrared light, radio and microwave radiation, X-rays and nuclear or cosmic radiation.

It may be used in bolometers, thermoelectric piles, pneumatic detectors, photoconductive cell detectors, scintillation counters, radar and maser detectors, television cameras, medical X-ray apparatus, astromonical apparatus, metascopes, image transformer tubes, sniperscopes, photographic cameras, spectrographic apparatus and solar furnaces.

Although researches directed at perfecting the radiation sensitive elements of such instruments and the associated devices, which may be of an electronic nature, have been pushed very far, on the contrary it appears that, apart from photographic devices and solar furnaces, insufficient attention has heretofore been paid to the frontal optical elements used in receivers. One sees even now, for example, otherwise highly perfected radiation detectors in which the front receiver is a simple window transparent to the radiation being detected, such as a plate with parallel or lightly curved faces without well defined optical characteristics. Thus the problem of the maximum optical concentration of a flux of radiant energy under the given conditions has not been solved or even posed.

Nevertheless it is clear that what is of primary importance for the efiiciency of a receiver is the quantity of radiation utilized per unit of sensing surface, that is,

3,535,016 Patented Oct. 20, 1970 the concentration of energy provided at the transducing element by the frontal radiation interceptor. The quotient of radiation energy flux at the sensing surface is the energy ilumination thereof and it must be emphasized that in general it is this value which is essential and not the total quantity of radiation intercepted. For example, a small photographic apparatus having a front lens 3 cm. in diameter and an aperture of F/ 2 intercepts less light than a large apparatus having a front lens of 5 cm. diameter and F/ 4 aperture. Nevertheless, the small camera would be four times as eflicient, the illumination of the photographic plate at each element of the image being four times as large for an aperture of F/.2 as for one of F/4, as is well-known.

Further, the interest in obtaining the greatest possible concentration of radiated energy per unit of sensitive surface of the receiver increases as the intensity of radiation available decreases. This is the case, for example, in the detection of natural infrared radiation emitted by objects and by human beings at a distance by day as well as by night or in the detection of a distant engine by a scanning head, or again for vision or photography in twilight or nocturnal conditions. It is particularly the case in the military field in the use of image transduction tubes or vidicons at night. In these areas electronic means for multiplying as greatly as possible the intensity of residual nocturnal radiation are used. In a moonless night under a covered sky, objects present a luminance of very low energy, of the order of 10* NIT (candles per square meter) of visible light, on the average, which is not detectable by the eye or by a presently available detector. If this luminance could be multiplied anly times, an intensity of 10* NIT would be obtained which is that of the same objects in full moonlight. If multiplied by 100,000 a level of luminance of the order of a NIT would be obtained which is that of objects at twilight or of a properly illuminated television screen. This involves the solution of a problem of great civil and military importance: to see without being seen. Examples could be multiplied in all fields of pure science and in their applications of all kinds (notably in the field of utilization of solar energy) where the necessity of obtaining the maximum concentration of energy by means of the frontal interceptor of energy is clear and imperative.

The term bidiopter is used hereinafter to designate generically reflective optical elements as distinguished from refractive elements and particularly to designate internally reflective frustoconical mirrors and frustoconical fiber optical elements.

The principle of the present invention by means of which this problem is solved and representative embodiments of those principles will be more particularly described with reference to the accompanying drawings in which:

FIGS. 1 and 2 are diagrams illustrating the general description of the principles of the invention;

FIG. 3 is a diagram illustrating the discussion of tapered fiber optics;

FIG. 4 is a diagrammatic longitudinal section of a frustoconical bidiopter;

FIGS. 5 through 10 are fragmentary details illustrating aspects of the frustoconical bidiopter of FIG. 4;

FIGS. 11 through 13 are diagrammatic illustrations of the combination of a frontal convergent system with the bidiopter of FIG. 4;

FIG. 14 is a diagram of an afocal system;

FIG. 15 is a diagram of the combination of an afocal frontal system with a frustoconical bidiopter;

FIG. 16 is a diagram of a folded bidiopter embodying the principles of the invention;

FIG. 17 is a diagram of a thermistor bolometer embodying the principles of the invention;

FIG. 18 is a diagram of a concentrator coupled with a centimeter wave detector;

FIG. 19 is a diagram of a detector including means for sweep scanning of the field;

FIG. 20 is a diagram of a metascope embodying the principles of the invention;

FIG. 21 is a diagram of a solar furnace embodying the principles of the invention; and

FIG. 22 is a diagram of a rotator for the solar furnace of FIG. 21.

A convergent lens system forming an objective is characterized by relative aperture l/N defined as the ratio of the diameter 2R of the front pupil to the focal distance F:

The objective is said to have an aperture F N For a distant object of luminance B, such an objective forms in its focal plane a real image, the illumination E of which is [(in candelas or new candles) B(iI1 NITS) 5 111 square meters) If an object radiates uniformly in a demi-space a flux l (in lumens), the radiance R of the object (in lumens per m?) is the quotient of the flux by the emitting surface S, that is, the surface density of the emitted fiux.

The luminance B is related to the radiance by the formula B=R/1r From Formulas 1 and 2 the relation between the radiance R of an object uniformly radiating in a demi-space and the illumination E of its image formed by a photographic objective is seen to be:

R E T 4N2 As it is known that the theortical limit of the aperture of a photographic objective has the maximum value 0.5, it results that for an object of given radiance R the illumination of its real image provided by a lentieular objective has a maximum value lirn. Err/ 1 4 R ($9 or, given the transparence T of the objective at maximum value 1 Thus, the maximum concentration of a luminous flux by means of an objective lens system is attained when the illumination of the image has the same value as the radiance of the object, that is to say, when the quantity of fiux received per unit surface of the image is equal to the quantity of fiux emitted per unit surface of the object.

It is well known that this limit is not accessible in practice. Exceptional objective len systems of apertre F/ 0.59 have been realized but it is not simple to exceed F/ 1. A good current aperture is F/3 which corresponds to that of the human eye at night and to the objectives currently used in image intensifier tubes. At the aperture F/ 3 the concentration of radiant flux is 36 times smaller than the theoretical maximum concentration.

Referring to FIG. 1, if one considers a pencil of solid angle dw formed of rays impinging on an element of a source of radiant energy of surface ds in a medium of optical index 11 the normal to which makes an angle 0 with the mean axis of the pencil and a pencil of solid angle dw' emerging from a medium of index 11 after havlim. lip 12 ing undergone any number of refractions or reflections in an intermediate optical system schematically represented at 0 and supposed to be nonabsorbent (neither diffusing or ditfracting) one has, designating as ds the elementary surface of the minimum section of the pencil the normal of which makes an angle 0 with the mean axis of the pencil, the Clausius relation:

The application of this relation is not limited to the optics of light. It applies to all electromagnetic radiation and the photometric interpretation must be made with the use of energy values (energetic luminance, energetic illumination, etc.).

The photometric significance of this relation may be found b writing dsclw cos 6 n dsdw cos 0I 77/I2 Since the energetic luminance B of a source element of surface ds is:

5P tlsdw cos 0 (the letter P representing the transformed flux) and the energetic luminance B of an element of image or of irradiated surface of surface ds is therefore B dsdw cos 0 B dsdw cos 0 B' m B 21112 5) 77.0 Beg-1,. Re

The interest of the Clausius relation resides in the fact that it is of the most general application in physics. Not only is it valid for all possible optical systems but it arose from thermodynamic studies as a corollary of the principle of Carnot and presents a bar against all attempts to increase without limit the illumination of the image. But, although reasearch in that direction is thus definitely limited it has been found possible to define two possibilities which are far from being negligible: the first relates to the factor z/ z includede in the invariance relation; the second results from thermodynamic consideration related to the principle of Carnot and to optical exchanges between black bodies.

The first possibility is the expedient of immersion. In a medium of index a given flux is radiated in a solid angle 11 times smaller than in air. But according to another law of thermodynamics, also due to Clausius, the emissive power of a black body increases in direct proportion to the square of the index of refraction. The last optical medium in contact with the sensing element must then have an index as high as possible for the mean wave length of the radiation to be concentrated. Furthermore,

the optical system used should be capable of obtaining in addition to all else the benefit of the n factor, that is, of obtaining a concentration It times as great as by means of a system of theoretical aperture F 0.5.

The second possibility makes possible an increase up to double the energetic illumination calculated in conformity with the conservation of luminance:

Traditional optical systems only transmit or concentrate radiation within 27r steradians, that is, in a demispace. However, a black body can receive radiant energy over 41r steradians. Consequently, the traditional optical systems loose at least half of the radiant energy which it is possible to concentrate on a black body in the given conditions.

Optical concentrators operating over 41r steradians instead of 21r steradians are described in applicants application Ser. No. 424,341 filed Jan. 8, 1965, now abandoned.

By combining this possibility with that of the n factor previously defined, it can be concluded that the maximum power which can be concentrated on a given element, immersed in a medium of index n, is 2n times as great as the power which would be concentrated on the same element by a convergent optical system of aperture F/0.5.

If R is the energetic radiance of an object emitting radiation in air and 2E the sum of energetic illuminations produced by all concentrations of fiux from that object on a sensitive point element immersed in a medium of index n To indicate what that possible absolute concentration represents in relation to usual optic combinations some figures will be given. In comparison to the concentration obtained with a convergent system of aperture F/3 the absolute maximum concentration is 72 n times as great. With a concentrator of ordinary glass (11:1.5) it would thus be 162 times as great. With an infrared concentrator of germanium (n=4) it would be 1,152 times as great. In comparison with the minimum concentration obtained by exposing the sensing element directly to radiation (or through a plate with parallel faces having anti-reflective coatings), the proportion can be established as follows:

Consider a source element of apparent diameter 50:, of luminance B, illuminating one face only of a sensing surface in air, the normal to the surface making an angle with the direction of the source. Each point of the sensing surface receives a flux of radiation in a solid angle 6 of which the apex angle is equal to 50c. From photometry, it is known that the illumination E received by the sensing surface is E==Bdw cos 0 The luminance B being invariant, the maximum concentration corresponds to a solid angle .(2 of value 21r steradians (a demi-space) as if the sensitive element were at the center of a semi-sphere of uniform luminance B. Integrating B dw cos 0 from 0 to 21r gives the value B1r which is the maximum illumination.

Since the illumination received directly by the sensing surface assumed normal to the direction of the suorce (cos 0:1) is B80; the ratio of the concentrations is Expressing the solid angle So as a function of its demiangle at the apex 11/2 one has If a is small cos a/ 2 can be replaced by 6 whence 2 5w=21r and l i 5w ot Otherwise stated, a flux of radiation received in an apparent angle a can be concentrated in air to a limit ratio:

4: I/maL Z Concentrating the flux simultaneously on the two faces of the sensing element the concentrating effect is double and the absolute value of the limit ratio is l/absolute g For example, if radiation from the sun (apparent minimum diameter at equinoxes: 31'32") by means of a concentrator acting in air on one demi-space only of a transducing element, the limit ratio of concentration is (to a near approximation) 47,536. At the present time the greatest concentration which has been effectively realized in a solar furnaces is of the order of 20,000. Acting in 41r radians (on the two faces of a sensing element simultaneously) it is possible to obtain a double heating effect, the limit-ratio of which amounts to 95,072.

If a black body is submitted to such a maximum concentration the absolute temperature which it would theoretically attain in the limit, the temperaure corresponding to the radiance of the sun viewed directly through the atmosphere, would be between 5,200 and 5,80() K. (at Zenith at latitude 45).

Including the factor 12 due to immersion, the limit ratio between the maximum energetic-effect of concentration and the effect of direct reception of the flux of radiant energy, in the case of concentration on only one face of the sensing element the value:

and by concentrating the flux simultaneously on both faces of the sensing element the doubled value:

In the case of an abundant and very energetic radiation such as solar radiation one would be limited practically in the use of immersion by the fusion and thermal destruction of the optical materials used. On the contrary in the case of concentration of radiation of low intensity or energy (as in detection devices) the value of the limit ratio takes its full significance.

With a concentrator of ordinary glass (11:15) and apparent diameter of radian (about 30') the limit ratio of concentration,

attains 180,000. With a concentrator of germanium (11:4) it attains about 1,300,000. For a source of apparent diam eter of 3 or radian (for example a source of 1 meter real diameter detected at 1 km.) the ratios have values of over 18 millions as about millions.

The absolute maximum possibilities of the concentration of given flux of radiant energy being thus clearly established it is manifest that the results obtained by means of the traditional optical combination remain far below the possibilities.

The purpose of the present invention is to remedy that deficiency and, to that end, the principle object of the invention is to provide an optical concentrating apparatus permitting the attainment of a maximum energetic illumination on the sensing element of a radiation receiver characterized by the following features alone or in combination:

(1) The optical device comprises essentially in combination: a front optical concentrating system of aperture l/N which receives a radiation fiux from a spaced source supposed situated in air and which effects a first concentration of the flux forming a convergent beam the rays of which have a maximum angle 6 to the optical axis of the system, sin 6 having a value of the order of 1/2N; and at least one frustoconical mirror, or an equivalent optical element, the apical half-angle 'y of the mirror being small, of the order of radian as a maximum, which effects a second concentration by means of internal reflections from the conical lateral surface, the large entrance face having a maximum diameter d positioned at the minimum cross section of the beam concentrated by the front optical concentrating system, and the small section, associated with a radiation sensing element positioned in the plane where the beam attains its maximum concentration, having a minimum diameter a' the value of which is determined by the formula Fir-E 2 wherein the large E denotes the integral part of the expression in brackets, 11 being the index of refraction of the internal medium of the frustoconical mirror, 11 being the index of the medium in optical contact with the sensing element at the small section of the frustoconical mirror, and being the angle defined by the relation the quantities n n sin 0 and tan 6 being also related by Arc sin B sin 0 B =Arc sin I:

71,1 1+ sin 0 1mm 7 in which 1; represents the minimum energy yield to be provided by the concentrator in relation to the absolute maximum concentration defined by the expression:

n Sin 6 (2) The device according to (1) comprises at least one frustoconical mirror consisting of a bidiopter in which the internal reflections are exclusively total reflections, the minimum diameter d being determined by the relation given in (1) in which the number p is not more than the maximum number q of total reflection determined the relation:

the quantities I1 sin 0 and 6 being also related by l 1 2 cos 2 n2 -s1n2v l n cos v+ 1-sm 7 sun 0 in which 77 represents the minimum energy yield to be provided by the concentrator in relation to the absolute maximum concentration corresponding to that specification of the concentrator and defined by the expression:

77/1 sin 0 (3) The device according to (1) 0r (2) comprises a bundle of bidiopter frustoconical mirrors, the large entrance faces of which are positioned in the same plane and in coincidence with the minimum cross section of a beam concentrated by the front optical concentrating system likewise positioned in the same plane.

(4) The device according to (1) or (2) comprises a plurality of serially arranged frustoconical mirrors or diopters, the first of which, of index n having its large entrance face, diameter d being positioned at the front optical concentrating system of aperture l/N, the second, having an index 11'}, greater than 12 and having its large entrance face in coincidence With the minimum section of the first, the third, having an index n larger than it" and having its large entrance face in coincidence with the minimum section of the second and so on, the apex angles of the respective mirrors or bidiopters being equal or not, the minimum section of the last mirror or diopter, in which the flux attains its maximum concentration being associated with a radiation sensitive element immersed in a medium of index 11 and having a diameter d such that the ratio d /d for the ensemble of serial mirrors or diopters to the same specifications as defined in (1) for a single mirror or diopter, that is, that the ratio has a value as near as possible to the absolute minimum value:

(5) The device according to (1), (2) or (4) comprises at least one frustoconical mirror or bidiopter having sections cut, preferably at 45 to the axis, to permit folding back on each other as in prismatic optical instruments.

(6) The device comprises in series: a first bundle of frustoconical mirrors or bidiopters according to (3) and one or more mirrors or bidiopters according to (1), (2), (4) or (5) wherein the large entrance face of the first of the mirrors or bidiopters is in coincidence with the ensemble of adjacent minimum sections of the first bundle.

(7) The device comprises a plurality of bundles of frustoconical mirrors or bidiopters according to (3) positioned in series according to the characteristics defined in (4).

(8) The device according to (1), (2), (4), (5) or (6) comprises conic or conoidal, not of revolution, mirrors or bidiopters, wherein the ratio of the areas of the large entrance face and of the minimum small base, in the plane containing the optical axis is in all cases equal to the square of the ratio d /d specified in (1), (2) or (4), the maximum number of internal reflections being determined by the value assumed for the half'angle in the longitudinal section effecting the greatest linear reduction.

(9) The device according to (3) or (7) comprises a bundle or a series of bundles of frustoconical mirrors or bidiopters arranged according to (8), that is, so that the area of the ensemble of large entrance faces and the area of the ensemble of minimum sections are in the ratio defined in (8).

(10) Two devices according to (l) or (9) are arranged in parallel, the small bases of minimum section of their last frustoconical mirrors or bidiopters are associated respectively, by any known means, with each of the two faces of the same sensing element, the latter being preferably a thin plate.

The general type of the radiation concentrators of the invention have been determined a priori by the theoretical principles conceived by applicant which are briefly explained in the following.

An optical concentrator presents an extrance pupil of surf ace s and a terminal pupil of surface s (with s' s).

It receives a flux in a solid angle w and it finally concentrates the flux in a solid angle to. For maximum concentration the ratio s/s' must be as large as possible. Moreover, the concentrator, like any optical system, is governed by the Clausius relation. The most direct Way of establishing a formula characterizing the concentrator and not neglecting any of the data of the problem is to carry out an integration of the Clausius invariant, n cos fldSdw, taking care to fix the conditions of integration so that the conditions necessary for a maximum concentration are included.

Referring to the diagram of FIG. 2, consider dw, the elementary solid angle of emission, as the difference of the solid angles of the two nested cones having respectively the half angles at the apex and 0+d0. For every plane section perpendicmar to the common axis of the cones, 0 represents thus the angle which is made by the normal to the element of the section with the direction of the corresponding elementary pencil of rays. The element of surface ds is taken as the diiference of the right sections of the nested cones in the plane of the entrance pupil. An analogous diagram bringing in two nested cones having respectively, the apical demi-angles 0' and 0|d0 (not represented in the figures) is proposed for (1a), the elementary terminal solid angle and for ds', the element of surface of the minimum section of the last pencil.

The ensembles thus considered are figures of revolution about their optical axes which restrains very little the generality of the treatment. On the contrary the schemes proposed for integration imply the supplemental restrictive hypotheses which express the necessary conditions for a maximum concentration: the elements ds are all connected and do not overlap and the same is true of the elements ds and all of the elements dw and dc).

The surfaces s of the circles are replaced by the expression 1r/ 412 as a function of their diameter a; and the solid angles to by the expressions 21r(lCOS 0) as a function of the demi-angle 0 at the apex of the cone, giving 11 cos 0 dsdw=n cos 01ra/2dad[21r(lcos 0)] m cos 6 dsdw=1r m a cos 6 sin Odfida which is integrated according to:

1r 7L a cos 0 sin 0d0da the domain (D) being defined for a varying from 0 to d (diameter of the entrance pupil of the system) and for 0 varying from 0 to 6 (the maximum value).

This gives C11 61 i fl a dull cos 9 S111 6d0 The same reasoning may be applied to the invariant m d sin 0 at the terminal part of the system in a domain (D) defined for a varying from 0 to d the diameter of the terminal pupil of the system and 6' varying from 0 to 0 the maximum value giving finally, all of the quantities being positive:

n d sin 6 =n d sin 0 optics of the conical type (tapered fibers). This is not surprising since a tapered fiber constitutes the most simple of the aplanatic systems. At the limit, if the sections of entrance and exit of such a fiber become infinitely small they constitute a perfectly stigmatic system whatever the angle of the entering rays, that is without regard for the conditions of Gauss. This is not true of any of the other known convergent optical systems such as combinations of lenses, diopters or mirrors; they can only be aplanatic for paraxial rays, or in the immediate vicinity of one of their two points of absolute stigmatism (such as the points of Weierstrasse, for example, for a spherical diopter). The fact that a fiber does not transmit an image like the other traditional systems should not be illusory. A bundle of conical fibers can provide an image theoretically as fine as desired, surpassing thus in theoretical stigmatism all other known systems, without any regard for the conditions of Gauss.

The case of conical fibers is therefore preferred for the problem of maximum concentration of a radiation fiux. Their properties are briefly recalled with reference to FIG. 3.

Consider a conical fiber with large entrance face of diameter a and small exit face of diameter d A ray entering at an angle 6 to the axis leaves at angle 6 after having undergone a series of total reflections in the fiber. In its usual mode of use the fiber is immersed in air and its index of refraction is not involved. The general formula is well known and is found, for example, in the Fiber Optics Handbook, published in 1961 by the American Optical Company, Southbridge, Massachusetts:

It will be seen that the length of the fiber is not involved, any more than the precise form of its longitudinal profile, provided that the length is very large in comparison with the mean section. In reality, formula (13) expresses a limit relation, exact only for a fiber of infinite length and approximately satisfied for a very long fiber. It would be entirely false for a cone in the ordinary sense. The authors do not indicate any limits for the correct application of the formula. In the usual conical fibers the half-angle at the tip has a very low mean value (a few minutes of arc or value of the order of radian). But the curving shape arising from the drawing of the fibers renders imprecise the notion of a mean value of the halfangle at the tip.

To obtain images a large number of conical fibers are associated to form a tapered fiber bundle.- Thus the flux from an object is analysed by the mosaic formed by the large entrance sections of the flux and an image is formed by the mosaic of the small exit sections. To cite a current- 1y encountered example, the bundle of fibers would comprise 25,000 conical fibers each having a large entrance d sin 0 =d sin 0 face 250 microns in diameter and a length of mm. In

this example, the ratio of the diameter is 5 and the ratio of concentration of light is 25.

The conical fibers thus appear, at first view, to be fully indicated for the concentration of a flux of radiant energy. However, in the actual state of fiber optics technique and of the techniques which use them, some observations must be made which limit or even obstruct this sort of use.

To begin with, there cannot be any question of using conical fibers directly to concentrate a luminous flux from a distant source. Their length would be inordinate. If one wants to concentrate a flux in a field of 8 with an elfficiency of the same order as that of a theoretical convergent system of aperture F/ 0.5 with a bundle of 20,000 conical fibers each having a diameter of 50 microns at the exit, one would need fibers 40 meters in length with an entrance diameter of 100 mm. for each fiber and 16 meters for the entire bundle-as a simple calculation will show (introducing the concentration ratio 4/ a in Formula 8 with, here,

OLZSU/I6OZJAOOO radian for each fiber). If one associates the conical fibers with a convergent optical system to reduce their length, one would be on the way to a more acceptable solution. Nevertheless an empirical association would not furnish the best combinations assuring maximum concentration. Many factors come into play, notably, simplicity and cost of producing practical systems. The problem will be treated hereinafter in a complete manner and the solutions utilizing conical fibers will be proposed and constitute the particular application of the invention.

Further, the fact n authorized by the Clausius relation and present in the formula which results from its integration, is absent from the general formula of conical fibers. These are generally used in air. The problem of immersing the sensing elements in the fibers and its diverse implictaions is to be studied and will be returned to as a particular case of application of the invention.

Finally, the technique and the applications of fiber optics are ancillary to the technology of drawn glass. Actually, fibers have been conceived essentially in connection with visible light and, in a strict sense, with the near infrared. But in these domains more notable materials, such as germanium for example, cannot be drawn into fibers like glass. The present conception of conical fibers is here again not adapted for utilization as a concentrator of radiation.

One must conclude from these remarks that it is necessary to pursue the problem further and to generalize the conception of a total reflection concentrator, which has been retained, according to the integration of the Clausius relation, as being the most simple and the most direct, and of which the conical glass fibers represent only a particular example.

Such a concentrator can be defined in general terms as a frustoconical diopter, that is, a truncated cone of refractive material, having a large flux receiving right section, a minimum right section where the flux attains its greatest concentration, and a lateral conic surface whereby the radiation is concentrated by internal reflections. In its more general aspect the internal reflections do not have to be total reflections, but may be reflections from a lateral mirror surface, such as a metallic coating. In a further general aspect, the concentrator may be a conical mirror, the index of the interior medium having the value 1, in which case it is a simple mirror, or a value greater than 1, in which case it is a bidiopter, and the term frustoconical mirror is used herein to include mirrors in the more limited sense and bidiopters, according to whether the index of the interior medium is l or greater than 1. The mirror or the bidiopter may have an internal surface which is longitudinally arched, having substantially the same optical effect as a conical surface, as is the case with drawn glass fibers. The lateral surfaces need not be true surfaces of revolution; the right sections being, for example, elliptical, or the lateral surface may be conoidal and transform a flux of circular section into one concentrated into a rectilinear section. Only the bidiopters which are frustocones of revolution will be considered in detail and will serve as models for all the others, these being the form of frustoconical concentrators most frequently used.

The determination of the characteristics of truncated cones best adapted to attain the maximum concentration of radiation will be more fully discussed with reference to FIGS. 4 through 10.

The bidiopter 1, of index of refraction n is cut from a cone of revolution of apex S and apex demi-angle 7. It presents a large flux receiving face 2, of diameter d a conical lateral surface 3 and a small face 4 of minimum diameter d where the flux attains its greatest concentration. The received flux 5, supposed in air, is a pencil of rays whose maximum inclination to the optical axis is the angle 0 The value (1 of the diameter of the small face 4 and, at the same time, the ratio of the maximum concentration of flux (l /d is to be determined. To avoid confusing different problems, the first part of the discussion will consider only the progression of the rays in the interior of the cone, eliminating consideration of conditions of total reflection which will be considered subsequently.

It is evident that in a cone, any ray entering a right section (and not passing through the apex, a very particular case) will progress by a certain number of reflections from the lateral surface of the cone up to a certain limit at which the ray reverses upon itself and leaves the cone by the same section through which it entered. It can easily be shown that the ray progresses the less far in the cone, the nearer it is to the circumference of the right section and the greater its inclination to the optical axis. For a received pencil 5 (FIG. 4) the less favored rays are those such as 6, having a maximum inclination 0 to the axis and entering near the edge of the large face 2. The course of ray 6 is calculated with assurance that, if it attains as certain minimum right section, all other received rays will also attain it.

Referring to FIG. 5 which shows in detail on a very large scale a ray 6 entering large face 2 at point A near its circular edge and being refracted inclination to the axis having a value 0 such that 12 sin 0 =sin 0 The refracted ray strikes the side of the cone for the first time at 5 After reflection (total) at this surface its new inclination to the axis is [3 This angle will be important in the calculations and its value is easily established. On FIG. 5, 0 '+'y=,B y (by reflection) whence fl =6 +2y and since li Arc sin (sin 0 /Iz )(by refraction),

51=Arc sin l 7 (14) The inclination of the ray to the optical axis is thus augmented by 27 upon reflection from the surface of the cone. It is the same at each reflection and this is the fundamental phenomenon for the progression of the ray in the conic diopter.

Returning to FIG. 4, the ray 6 is reflected at successive points B B B on the surface of the cone up to a point B where, for the last time, it is reflected toward the apex of the cone. It finally strikes the lateral surface at point B and is reflected backwards, as detailed in FIG. 6.

The right section through B is then the minimum section of the cone attained by ray 6 and the value d of its diameter is now to be determined. All this is with reservation of the conditions for total reflection to be considered subsequently.

Designate by y the radius of the large receiving face 2, by y the radius of the right section passing through B and so on y y to y the radius of the right section through B and y the radius of the minimum section through B Designate by B B B B B, B the projections on the optic axis of points B B B B B respectively; by x x x x the distances B B B B B B B B and by C C C C the intersections with the axis of the segments B ,B B B B B B B respec tively.

Then in the right triangle 7 (FIG. 4)

and since, in the right triangle B C B and B C B 1=y1 Cot l ft-Y2 Cot 51 then l3 and y1( v cot B1) y2 l+tan 3 col? 5 or multiplying above and below by tan [3 tan B tan v y2 y1 tan B +tan 7 By the same reasoning tan B tan v yazyz tan li t-tan tan B tan 'y yp:yp 1 tan B +tan 'y from which :2] sin (Brw) 5111 [131+ t pm or in terms of the diameters (I and d This ratio is a function of ,8 and thus according to Equation 14, a function likewise of 0 of 'y, and of p. The number 2 represents exactly the maximum number of reflections which ray 6 (the least favorable of the received pencil) can make from the lateral conic surface without reversing. It remains to determine the value of the number p as a function of {i and 'y.

The ray 6, increasing its inclination to the optical axis by 2 at each reflection can be reflected (/i -B )/2v times between the points B and B that is in all (including reflection B The maximum value of p thus depends on the maximum value of [3 which is obviously 1r/ 2. The expression (1r/2- ,8 )/2'y does not in general represent a whole number and p must be taken as the integral part of which may be written Ei t l 1 The Formulas 14, 15 and 16 define the minimum value of the diameter d of the right section of the cone in which it is possible to concentrate all of the received flux under the given conditions. Denoting the absolute maximum concentration under these conditions by C'y/d we have:

$1112 [31+ z )"rl Cit/d2 s n (61-7) (1 For a sensing surface of the receiver to make full use of this maximum concentration it is necessary and sufficient that the sensing surface be immersed in the minimum right section and that it coincide therewith, its own diameter having the same value d The frustoconical bidiopter of maximum concentration having a receiving face of diameter d a small face of diameter d and an apical demi-angle v is thus fully defined for a given pencil of radiation of maximum inclination 0 But it is not always possible to immerse the sensing surface directly at the small face of the bidiopter. In many cases, it must be immersed in an intermediate optical medium the index of refraction 11 of which is smaller than the index n of the bidiopter. The small face can then no longer be the right section of diameter (1 since a certain number of the concentrated rays undergo a total reflection at the small face and cannot penetrate the medium of index 11 and reach the sensing surface. It becomes necessary to generalize the foregoing formulas to the case where the sensing surface is immersed in a medium of any refractive index The sensing element being positioned as close as possible to the small outlet face of the bidiopter, the maximum exit angle of ray 6 is 1r/2 (see FIG. 7). The maximum angle of incidence of ray 6 on the outlet face in the in terior of the bidiopter is Mz n the angle of total reflection of a medium of index n with respect to a medium of index 12 so Mz /n =Arc sin (H /n The maximum value of angle [3 is then likewise in this case: Arc sin n /n (FIG. 7) and denoting by p the maximum number of reflections that ray 6 can undergo from the lateral surface of the frustocone:

Arc sin (Hg/1L1) sin (Brv) The corresponding maximum concentration is:

X sin fl 'y) The relation 19 together with relations 14 and 18 suffice to characterize all the possible frustoconical mirrors or bidiopters. The concept of maximum concentration of a given flux is thus not absolute but is relative to the value 11 of the index of refraction of the last medium in optical contact with the sensing element of the receiver. The least favorable case is that where 11 :1, that is, the case where the sensing element is immersed in air. In this case the expression Arc sin 11 /11 in the general Forumla 18 by the known value of the angle M1 of total reflection in the medium of the bidiopter giving:

El EI l 1) Denoting by (1 the minimum value of the diameter of the small face in this particular case Formula 19 becomes:

d 5in (2271 1 3 sin (fli'y) (22) and the maximum concentration C'y/d is:

Sil12 [31+ P1' W] O'Y/d3 s nz (B1 Y) The most favorable case is that in which :11 that is to say the case in which the sensing element is immersed directly on the small face of the bidiopter, and the more so the greater the refractive index 12 It is only limited by the properties of the available materials and the conditions of the application in view. It should be noted that in every case where n n the index 11 of the bidiopter does not itself have any effect on the theoretical maximum 5 may be transposed. This condition is clearly that the angle of incidence of ray 6 on the lateral conical surface is greater or at least equal to the angle of total reflection in the medium of the bidiopter, or M1 in the general case where the surface is bathed in air. Referring to FIG. 8, it will be seen that this condition implies for the angle [3,, corresponding to the last point of total reflection B at -a a The letter q designates here the maximum number of total reflections. In the case where the surface of the bidiopter is not bathed in air but in a medium of index 11 (a sheathed bidiopter, for example), the angle M1 is replaced, in Equation 24 by:

whence Are sin 11 /11 Comparing Formulas 16 and 24 it will be seen that the maximum number p of reflections in the case of immersion in the bidiopter is larger than the number q of possible total reflections. In effect, M2 is in general larger than 3 since 7 cannot, as will be seen below, exceed a few degrees in practice, while N1 is at least equal to about fifteen degrees (for 11 :4, for example in the case of germanium). Therefore, one would not fully benefit from the maximum concentration permitted by immersion of the sensitive element in the bidiopter, if one were restricted to the use of natural total reflection. To benefit nearly to the point of loss by absorption, from that maximum concentration it is necessary to use a reflective coating (silver, gold, aluminum, or other) on the terminal portion of the lateral frustoconical surface between the points Bq-l-l (FIG. 8) and Bp+l (FIG. 6), that is, between sections 8 and 4.

Denoting by (1 the minimum value of the diameter of the right section passing through point Bq+1, Formula 19 becomes:

1 sin (aw) 5) and the maximum concentration C y/d corresponding to the smallest right section attained by total reflection is:

The section of diameter d plays an important role. In practice, it most often forms the minimum section of the bidiopter. On the one hand, in effect, the concentration C /d has a value approaching the absolute maximum concentration C' /d as the index n becomes greater; and on the other hand the necessity for immersing sensing element of the receiver in a medium of index 11 lower than that of the bidiopter, usually makes it useless to push the concentration beyond that of C'y/d The use of silvering or other reflective coating (the same as using a frustoconical mirror in place of a bidiopter) is moreover subject to a loss by absorption, weak at each reflection but becoming considerable for a large number of reflections. On the contrary total reflection occurs practically without energy loss. It is known that for a normally polished surface, the radiation diffused to the exterior on total reflection is spread out in a plume of which the maximum energy content is of the order of 0.5 -10 After total reflections, the loss of energy in the least favorable direction is of the order of 0.5%.

FIG. 9 summarizes the results obtained for the unique values d d d and d of the diameter of the minimum section of a diopter. For an apical angle of the given cone, 2 and a pencil of radiation of given angular aperture 20 a frustoconical bidiopter of index 11 at maximum concentration has its small face at a minimum section of which the diameter a lies between the extreme values: 0' and d The value d the largest of all, corresponds to the small face of a bidiopter for which all of the rays of a pencil of radiation are allowed to escape into the air after maximum concentration. The value d the smallest of all, corresponds to the small face of a bidiopter for which none of the rays are allowed to escape into the air or into any optical medium of lower index than that of the bidiopter. Between these two extreme values, all of the intermediate values a are possible, corresponding to maximum concentrations in all the cases where the pencil of radiation is allowed to escape in a medium of index 11 (of value between 1 and n Among these intermediate values, the value d corresponds to the minimum section for which total reflection at the lateral surface of the truncated cone is possible.

It remains, in order to have all of the characteristics of the frustoconical mirrors or bidiopters of maximum concentration included in the radiation concentrating apparatus of the invention, to calculate the length of the frustum of the cone L This value is readily deduced from the general Formula 19:

This formula may usefully be transformed into:

2 tan 7 The last formula permits the calculation of the length of the frustoconical mirror or bidiopter from the diameter d of this minimum section. If this minimum section is to be associated with the sensing surface of a receiver, the Value d also must be that of the diameter of the assoelated sensing surface, a value which is most often the essential design datum of the apparatus. Formula 28 is therefore of great practical interest.

In an analogous manner the lengths of the bidiopter of the form: L'y/d L'y/d L'y/d corresponding to the diameters d d d respectively, are defined. It is to be noted that if a bidiopter (or a frustoconical mirror) is given an actual length greater than the length calculated by means of one of these formulas, the concentration is not much affected. In fact, the loss due to the rays which revert towards the entrance face is nearly compensated by the gain due to the fact that the area of the minimum section is reduced. For a small excess in length the concentration obtained is about the same. On the contrary if the bidiopter is given a length shorter than the calculated length, the concentration obtained is rapidly reduced. Care should be taken therefore in the construction of a bidiopter that any error in length should be in the direction of greater rather than lesser lengths than those calculated by the formulas.

All of the Formulas -18 calculated above have been exact formulas, that is, they do not incorporate any approximations. They characterize completely all of possible frustoconical mirrors or bidiopters of maximum concentration on the basis of their apical demi-angle However, simplified formulas, especially for carrying out a succession of calculations and for rapidly determining optimum combinations involving a variety of parameters may be used.

A first simplification can be made when the expression in formula 18 is an integer or nearly an integer because the maximum number of reflections p is quite large (that is, when the apical demi-angle is quite small).

This simplication can be established for the ratios ti /d d /d df/d and ti /d by designating as d d d and d the values of the minimum diameters thus simplified.

In the case of the minimum section of diameter d (maximum immersion) the expression for p (Formula 16) becomes whence P )'Y= fi1+v and, according to Formula 15:

It follows that a simplified expression for the maximum concentration C'y/d is 18 In the case of the minimum section of diameter d (the general case of immersion of the sensing element in a medium of index n the expression p Formula 18) becomes I Sin 2/ 1)f 1 7 whence i m /n (cos 2y+ /n /n l-sin 27)+sin 27 C"y/d 2 S111 (Bwv) In the case of the minimum section of diameter d (immersion in air; n =1) d 031/ 3 sm (6 (33) and for the concentration C'y/d C 1/'n (cos 2 /n l-sin 27) +sin l 3 S111 p 34) Finally, in the case of the minimum section of diameter d (limit section for total reflection) the expression for q (Formula 24) becomes:

cos (Mn-2 Sm (Bi-v) 5) and for the corresponding concentration, Ge /d cos (ATL1-2'y) iv/d4 T1 (I 1v) (36 Formulas 29 to 36 provide an excellent approximation. It has been found that the relative errors arising from their use are always less than 2 (even with an angle as great as radian the relative error is less than V of the length).

An even greater simplification is possible when the value of the apical demi-angle 'y may be considered as negligible, that is when the value tends to zero.

When 7 approaches zero, the limit values of d d d d.; are designated d d d and d.;.

In the case of the section of diameter d (absolute maxi-mum) the Formula 29 gives Since [3 =Arc sin sin 0 /n +2'y it follows that sin 5 approaches sin 0 /111 Hence:

d /d "=n /sin 91 and for the maximum limit concentration C /d lim. 'y- 0 0 /01 =C /0l "=n /sin 0 (38) In the general case of the section of diameter d Formula 31 gives Finally for the section of diameter d (limit for total reflection), Formula 35 gives:

cos kn,

sin M1 having the value 1/11 whence 2 1 1 dl/di sin (45) and for the maximum limit concentration, C /d n *l CL/di sin 0 (44) Formula 41 could have been derived from the general Formula 12 of conical fibers, adapted to the present notation:

d sin 6 =d sin 0 In effect, the concentration is maximal for the exit angle 0 equal to 1r/2 or for sin 0 :1 whence d sin 6 =d or This shows that the general formu a for conical fibers is the ideal formula which can only be true for a fiber of infinite length (7 approaching zero). The Formula 43 fixing the limit section for total reflection can also be calculated directly from the case of the conical fiber. Formulas 37 and 39 correspond to a generalization to fibers in the case of immersion which will be considered for bidiopters in the strict sense.

The conical fibers thus appear as a particular case or, more exactly, as a limit case of frustoconical bidiopters. To this extent they can be utilized in the receivers of the invention; the necessary condition being to give the diameter of the large flux receiving face and the diameter of the minimum section the respective value defined by relations 37, 39, 41 or 43.

The results derived from these formulas are set forth on FIG. 10 which represents, analogously to FIG. 9, a frustum of a conical fiber with sections d d d d, and which otherwise consist with the formulas for the concentrations and their relation to the theoretical limit concentration of a convergent system of aperture F/0.5.

There are particular cases of a quite different order for radiation very different from visible or infrared radiation. For example, the concentration of short or very short (radar) Hertzian waves requires according to the invention mirrors in the form of elongated metallic frustocones, the minimum section of which is associated with a dipole.

Knowing the characteristics of all of the frustoconical mirrors and bidiopters of maximum concentration and their approximations, the remaining problem to be solved will be apparent. In effect, leaving aside the special formulas where the apical demiangle 'y negligible approaching zero), all of the formulas and notably the formulas giving the relations of maximum concentration are expressed as a function of It is therefore essential to 20 ascertain precisely the effect of the value of 7 on the energy yield of frustoconical mirrors.

Taking for comparison the maximum concentrations given by conical fibers ('y approaching zero), it will be seen that they theoretically constitute, in each of the categories, the most favorable case. The ratios of the form C characterizing these concentrations have been established in the foregoing: C /d (Formula 38), C /d (40), C /d (42), C /a' (44). The problem is to compare with them the relations of the form C'y characterizing the concentrations in all of the cases where the value 7 of the apical demi-angle is not negligible, to know respectively: Cy/d (Formula 17) and C'y/d (Formula 30); C-, /d (20) and Cv/d (32), C'y/d (23) and Cv/d (34), C'y/d (26) and C'y/d (36).

Take, for example, the comparison between C'y/d and C /d The calculation for C'y/d is selected because it would be too time-consuming to treat each case in detail and because C'y/d (the case of maximum concentration for complete immersion in simplified form) is particularly useful. It involves comparing a frustoconical bidiopter of apical demi-angle 'y, with a large flux receiving face of diameter d accepting a pencil of angular aperture 0 with a conical fiber with a large flux receiving face of the same diameter d accepting the same pencil of the same angular aperture 6 To be established is the relation:

97/ 2 O/ Z To simplify the notation it will be convenient in the calculations to designate C'y/d by C7, simply, and C /a' by C According to Formula 30 cos '1 (B1 'Y) As B =Arc sin (sin 0 /n )+2-, (Formula 14) and as n /sin 0 /C (Formula 38) of Formula 46 represents, in the most general case, the energy yield of the bidiopter relative to the ideal concentration which would be realized if the value of its apical demi-angle 7 were nearly zero. This ratio may be directly expressed as a function of n n sin and tan 7 by replacing .C /d in Formula 46 by its value n /sin 9 and simplifying, giving Fixing a minimum 1; for the energy yield gives the relation:

C-,/d 1+ /(n /n )1-tan v Clo/ix, /(n /sin 0 l-tan 'y (48) which is the characteristic formula of frustoconical bidiopters and mirrors yielding a given minimum of the maximum concentration under given conditions.

The approximation of the Formula 46 is sufficient to calculate the yield.

In the case of a bidiopter of strictly total internal reflection the approximation of Formula 47 may be used:

( cos 27+ /l/(n1 -l)-sin 2 cos 7+\ (7 /Sin 0 )1-sin v 49) 1; is expressed as a number between 0 and 1 or as a percentage. Expressing, for example in Formula 48, 1 by 0.80 or by 80% signifies that the ratio or a yield of about 4% of the theoretical concentration. One therefore obtains an actual concentration of about 16 times.

If it is proposed to obtain with a cone of the same apical demi-angle ('y= /6 radian) the greatest possible concentration, C, would have to have a value in excess of 47,000 and Formula 46 would give for the value of C'y/C about: 0.0007. The yield would be less than 1% compared to the maximum theoretical concentration in air, that is compared to that of a convergent system of aperture F/0.5. Such a yield would be very much less than that of the most rudimentary parabolic mirror.

Thus if it is proposed to obtain with a frustoconical concentrator a minimum yield 1 amounting to a substantial proportion of the maximum theoretical concentration 22 the apical demi-angle 7 cannot have too great angle (the order of which will be shortly seen).

Next to be determined, by means of the formulas, is the best means of augmenting the value C'y/C as the apical demi-angle 'y is not the only parameter involved.

Three factors enter into the expressions of the ratio C'y/C First, tan as it will be designated. Next, the ideal reference concentration C which enters into the denominator of the ratio. Finally the yield is not the same as the yield r/ z 'o/ z which signifies that the ratio n /n is a factor.

Consideration of the last factor permits a judicious choice of the optical materials used in construction of the bidiopter and the immersion of the sensing element of the 7 receiver but it does not provide much latitude in impro ing the ratio C'y/C' In general, the yield is better than the yield except for relatively small values of C for which the relation is the inverse. There is thus more frequently a greater advantage in immersing the sensing element in the bidiopter than in choosing materials which make n and n as close as possible. The choice must be studied in each particular case.

As to the first factor, tan 7, its value can only be decreased with discretion. As Formula 27 shows the length of the bidiopter increases as tan 'y decreases. But this length can-not be made too great. The incumbrance, the weight and the cost of production present limits. Moreover, internal absorption ought not decrease the yield. Most materials used in the field of visible light or for other radiations have a low optical density and absorption is usually negligible even at considerable thickness. However, this problem which will be given further consideration may present difficulty with certain materials. There is thus in each case a limit to the possible diminution of the apical demi-angle.

The only remaining possibility is to work on the second factor, that is, to decrease the ratio C /d (or,

according to the case, C /d or C /d of the theoretical concentration required of the bidiopter. Since these ratios can be expressed as 11 sin 0 (40) n /sin 0 38 or (n 1)/sin 0 44 respectively, the solution is to increase the maximum inclination to the axis 0 of the received rays, that is to adjoin to the frustoconical bidiopter or mirror a frontal optical system effecting a preliminary first concentration. In this way the ratio of concentration required of the frustoconical bidiopter or mirror to obtain the maximum possible illumination of the sensing element is reduced which allows a greater latitude of choice of the value of the apical demi-angle 0.

The optical systems capable of effecting this preliminary concentration of a flux are of two kinds: convergent systems (objective lenses, diopters, mirrors) which furnish an image of the source in their focal plane, and certain afocal systems (telescope or spyglass type) in which all of the flux received through a large entrance pupil leaves by a small pupil or ocular circle without forming an image in the plane of the circle.

The combination with a convergent frontal system will be described first with reference to FIGS. 1113.

In FIG. 11, lenticular objective 9 has an aperture of diameter 2R and a focal image distance 1. Its relative aperture 1/ N is therefore This objective gives in focal plane 10 a real image of diameter 1' of a distant image of apparent diameter a:

izf' ot (a in radians and assumed small) The pencil of radiation which converges to form that image and which diverges on passing it has an apical demi angle the maximum value of which is designated by 61.

The energy concentration C, effected by the objective is measured by the ratio of the entrance surface to the image surface:

C (2R/i) Since ZR f/N and i=fcc C :1/N 0t (50) Since (Formula 10) the maximum concentration on an element immersed in a medium of index 11 is, for a pencil of rays of apparent angle a:

Cn /max.=4n /ot The associated frustoconical bidiopter must therefore effect a concentration C equal to the quotient of C max. by C or:

C 4:7l/2 /(X I1/N L1 Such a bidiopter 11 is represented schematically in FIG. 11. The large flux receiving face 12 is coplanar with the image formed in focal plane 10. The diameter of the large face, d is then equal to the diameter i of the image. The bidiopter receives all of the flux partially concentrated by the frontal objective. The diameter d of the minimum section 13 of the bidiopter, in which the maximum concentration of the fiux is effected, has a value given by Formula 19 taken with Formulas l4 and 18, as a function of the apical demi-angle a. A sensing element 14 is positioned at face 13 and is immersed in an optical medium of index n for example, a thin film 15.

In case the frontal convergent system is a diopter, the term diopter being used hereinafter to designate generically optical elements acting solely by reflection from a surface between two mediums having different indices of refractions, the immersion of the image, which augments the real relative aperture, must be taken into account. A spherical diopter of index 11, diameter of aperture 2R, and focal length f, has a nominal aperture Its real aperture is n times as great and the real aper- There have been schematically represented on FIG. 12 two spherical diopters D and D with indices 3/2 and 2 respectively, having the same real aperture (F/2) and the same geometric center C. These diopters give, in their common focal plane, the same image 1' of a source apparent diameter a. 1 designates the thin lens, of relative aperture F/2, equivalent to the two diopters: its optical center coincides with the center C of the diopters; its focal plane corresponds with that of the diopters. For an associated bidiopter the three convergent systems D D and l are equivalents.

Of course, all of the dioptric combinations used in the novel concentrators of the invention as well as the plane faces of the bidiopters are advantageously surface treated to suppress partial reflections detrimental to the energy yield. It is known that in the case of two optical media of optical indices n and 11 in contact, and for a given wavelength x, the application to the surface of separation of an anti-reflective layer of index /n n and a thickness or M4 (or an odd integral multiple thereof) will suppress nearly all partial reflections up to an angle of incidence of about 45 to the normal.

In the case, finally, where the frontal convergent system is a mirror, the arrangement is as shown in FIG. 13 which schematically represents the association of a spherical mirror 16 and a frustoconical bidiopter 17. The bidiopter is positioned ahead of the mirror. The latter has an entrance diameter 2R, a focal length 1 and a relative aperture l/N, which characteristics are assumed to be the same as those of the dioptric objective of FIG. 1, to facilitate comparison. Likewise, the maximum angle of inclination to the optical axis of the convergent pencil of rays formed by the mirror 16 is designated 0 The formulas established previously in the case of a lenticular objective are valid in the case of a mirror, notably Formula 51 determining the theoretical concentration C required of the associated bidiopter.

'In one case as in the other, the sine of the maximum angle of inclination 0, which is an important feature of the characteristic formulas of the associated bidiopter, has a value near to the ratio R/F sin 0 =l/2N (54) This formula is useful in facilitating the calculations in the present case, But the value 1/2N is only an approximation for sin 0 First this value is established in optical instruments for the mean angle of inclination of the rays of the convergent pencil and not for the maximum angle properly speaking. Also it is not valid for aplanatic systems. In the case of aplanatic systems (such as parabolic mirrors, for example) and in every case where a high precision is needed the exact value of sin 6 must be the object of a special calculation or measurement.

The frontal optical concentrating system may finally be constituted by an afocal system (of null convergence) which represents a separate case.

FIG. 14 represents an afocal system schematically reduced to a combination of two lenses 18 and 19, having a common focus designated F F Lens 18 has an opening of diameter 2R and a focal length f Lens 19 has a diameter 2R and a focal length f its second focus is desgnated F The optical centers of the lenses are designated by 0 and 0 respectively. 2R is taken greater than 2R The angle on at which lens 19 is seen from the optical center 0 of lens 18 is approximately the field of the afocal combination.

It is known that with such a combination all rays received in the field angle a by the entrance pupil of lens 18, pass finally through an exit pupil 20 of center 0 known as the ocular circle. The ocular circle is the real image of the lens 18 (entrance pupil) formed by lens 19 in a plane close to its focal plane.

Denoting by j the diameter of the ocular circle one has with relation to the optical center 0 of lens 19: 

